Combining isotonic regression and EM algorithm to predict genetic risk under monotonicity constraint

TL;DR

This paper introduces a new method combining EM algorithm and isotonic regression to accurately estimate disease risk over time in genetic studies, ensuring monotonicity and handling censored data.

Contribution

The paper presents a novel approach that integrates EM and isotonic regression to estimate cumulative genetic risk with monotonicity constraints from family data.

Findings

Successfully applied to Parkinson's disease data

Detected significant risk differences in mutation carriers

Ensured monotonic, nonnegative risk estimates

Abstract

In certain genetic studies, clinicians and genetic counselors are interested in estimating the cumulative risk of a disease for individuals with and without a rare deleterious mutation. Estimating the cumulative risk is difficult, however, when the estimates are based on family history data. Often, the genetic mutation status in many family members is unknown; instead, only estimated probabilities of a patient having a certain mutation status are available. Also, ages of disease-onset are subject to right censoring. Existing methods to estimate the cumulative risk using such family-based data only provide estimation at individual time points, and are not guaranteed to be monotonic or nonnegative. In this paper, we develop a novel method that combines Expectation-Maximization and isotonic regression to estimate the cumulative risk across the entire support. Our estimator is monotonic, satisfies self-consistent estimating equations and has high power in detecting differences between the cumulative risks of different populations. Application of our estimator to a Parkinson's disease (PD) study provides the age-at-onset distribution of PD in PARK2 mutation carriers and noncarriers, and reveals a significant difference between the distribution in compound heterozygous carriers compared to noncarriers, but not between heterozygous carriers and noncarriers.